In　practice,　the　performance　of　distribution　feeder　parameter　estimation　is　limited　by　the　measurement　conditions　in　distribution　networks.　An　accurate　mathematical　model　that　considers　limited　phasor　measurements　in　distribution　networks　is　necessary　to　estimate　feeder　parameters.　This　paper　presents　a　set　of　modified　parameter　estimation　models　for　unbalanced　three-phase　distribution　feeders　that　only　require　the　measurements　of　voltage　amplitudes　and　power　flows.　To　simplify　the　calculation　process　and　improve　the　estimated　results,　a　method　combined　with　a　radial　basis　function　neural　network　(RBFNN)　and　multi-run　optimization　method　(MRO),　namely　RBFNN-MRO,　is　proposed　to　calculate　the　parameters　of　distribution　feeders.　The　relationship　between　the　feeder　parameters　and　the　measurement　data　from　the　two　terminals　of　the　feeder　can　be　mapped　perfectly　using　the　RBFNN.　Furthermore,　the　random　errors　in　the　measurement　device　were　eliminated　using　the　proposed　RBFNN-MRO　algorithm.　The　RBFNN-MRO　algorithm　can　limit　the　number　of　neurons　in　the　hidden　layer　and　substantially　reduce　the　training　time　for　each　RBFNN.　The　feasibility　of　the　proposed　method　was　verified　using　four　IEEE　test　systems.　The　proposed　RBFNN-MRO　and　RBFNN　methods　were　compared　using　the　maximum　absolute　percentage　error　(MAPE)　curves.　The　results　reveal　that　the　proposed　RBFNN-MRO　method　has　excellent　potential　for　improving　the　accuracy　of　feeder　parameter　estimation　even　without　synchronized　phasor　measurement.